This is an accompaniment to Lecture 8. More on Linear Regression.
library(foreign) #To work with SPSS data
library(lmSupport)#Extra functions for linear model (may require install of nloptr also)
library(lm.beta)
library(stargazer)#pretty print regression output
##
## Please cite as:
## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(ppcor)
## Loading required package: MASS
##
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
##
## select
library(car)
## Loading required package: carData
##
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
##
## recode
#We are using our exam result dataset - regression.sav
#Read in the file
regression<- read.spss("regression.sav", use.value.labels=TRUE, max.value.labels=Inf, to.data.frame=TRUE)
First Model NormExam predicted by StandLRT
model1<-lm(regression$normexam~regression$standlrt)
anova(model1)
## Analysis of Variance Table
##
## Response: regression$normexam
## Df Sum Sq Mean Sq F value Pr(>F)
## regression$standlrt 1 1417.5 1417.50 2185 < 2.2e-16 ***
## Residuals 4057 2631.9 0.65
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(model1)
##
## Call:
## lm(formula = regression$normexam ~ regression$standlrt)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.65615 -0.51848 0.01264 0.54399 2.97399
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.001191 0.012642 -0.094 0.925
## regression$standlrt 0.595057 0.012730 46.744 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8054 on 4057 degrees of freedom
## Multiple R-squared: 0.35, Adjusted R-squared: 0.3499
## F-statistic: 2185 on 1 and 4057 DF, p-value: < 2.2e-16
lm.beta(model1)
##
## Call:
## lm(formula = regression$normexam ~ regression$standlrt)
##
## Standardized Coefficients::
## (Intercept) regression$standlrt
## 0.0000000 0.5916496
stargazer(model1, type="text") #Tidy output of all the required stats
##
## ===============================================
## Dependent variable:
## ---------------------------
## normexam
## -----------------------------------------------
## standlrt 0.595***
## (0.013)
##
## Constant -0.001
## (0.013)
##
## -----------------------------------------------
## Observations 4,059
## R2 0.350
## Adjusted R2 0.350
## Residual Std. Error 0.805 (df = 4057)
## F Statistic 2,185.011*** (df = 1; 4057)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Second model including dummy variable for gender
model2<-lm(regression$normexam~regression$standlrt+regression$girl)
anova(model2)
## Analysis of Variance Table
##
## Response: regression$normexam
## Df Sum Sq Mean Sq F value Pr(>F)
## regression$standlrt 1 1417.50 1417.50 2208.010 < 2.2e-16 ***
## regression$girl 1 28.06 28.06 43.704 4.317e-11 ***
## Residuals 4056 2603.88 0.64
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(model2)
##
## Call:
## lm(formula = regression$normexam ~ regression$standlrt + regression$girl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.56172 -0.51893 0.01808 0.53604 2.90399
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.10318 0.01990 -5.184 2.28e-07 ***
## regression$standlrt 0.59060 0.01268 46.571 < 2e-16 ***
## regression$girlgirl 0.16996 0.02571 6.611 4.32e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8012 on 4056 degrees of freedom
## Multiple R-squared: 0.357, Adjusted R-squared: 0.3567
## F-statistic: 1126 on 2 and 4056 DF, p-value: < 2.2e-16
stargazer(model2, type="text") #Tidy output of all the required stats
##
## ===============================================
## Dependent variable:
## ---------------------------
## normexam
## -----------------------------------------------
## standlrt 0.591***
## (0.013)
##
## girlgirl 0.170***
## (0.026)
##
## Constant -0.103***
## (0.020)
##
## -----------------------------------------------
## Observations 4,059
## R2 0.357
## Adjusted R2 0.357
## Residual Std. Error 0.801 (df = 4056)
## F Statistic 1,125.857*** (df = 2; 4056)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
stargazer(model1, model2, type="text") #Quick model comparison
##
## ===========================================================================
## Dependent variable:
## -------------------------------------------------------
## normexam
## (1) (2)
## ---------------------------------------------------------------------------
## standlrt 0.595*** 0.591***
## (0.013) (0.013)
##
## girlgirl 0.170***
## (0.026)
##
## Constant -0.001 -0.103***
## (0.013) (0.020)
##
## ---------------------------------------------------------------------------
## Observations 4,059 4,059
## R2 0.350 0.357
## Adjusted R2 0.350 0.357
## Residual Std. Error 0.805 (df = 4057) 0.801 (df = 4056)
## F Statistic 2,185.011*** (df = 1; 4057) 1,125.857*** (df = 2; 4056)
## ===========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Third model including interaction term (gender by standlrt)
model3<-lm(regression$normexam~regression$standlrt+regression$girl+regression$interaction)
stargazer(model3, type="text") #Tidy output of all the required stats
##
## ===============================================
## Dependent variable:
## ---------------------------
## normexam
## -----------------------------------------------
## standlrt 0.593***
## (0.019)
##
## girlgirl 0.170***
## (0.026)
##
## interaction -0.004
## (0.025)
##
## Constant -0.103***
## (0.020)
##
## -----------------------------------------------
## Observations 4,059
## R2 0.357
## Adjusted R2 0.357
## Residual Std. Error 0.801 (df = 4055)
## F Statistic 750.399*** (df = 3; 4055)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
stargazer(model2, model3, type="text") #Quick model comparison
##
## =========================================================================
## Dependent variable:
## -----------------------------------------------------
## normexam
## (1) (2)
## -------------------------------------------------------------------------
## standlrt 0.591*** 0.593***
## (0.013) (0.019)
##
## girlgirl 0.170*** 0.170***
## (0.026) (0.026)
##
## interaction -0.004
## (0.025)
##
## Constant -0.103*** -0.103***
## (0.020) (0.020)
##
## -------------------------------------------------------------------------
## Observations 4,059 4,059
## R2 0.357 0.357
## Adjusted R2 0.357 0.357
## Residual Std. Error 0.801 (df = 4056) 0.801 (df = 4055)
## F Statistic 1,125.857*** (df = 2; 4056) 750.399*** (df = 3; 4055)
## =========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01
Fourth model including dummy variables for school gender
model4<-lm(regression$normexam~regression$standlrt+regression$girl+regression$boys_sch+regression$girls_sch)
stargazer(model4, type="text") #Tidy output of all the required stats
##
## ===============================================
## Dependent variable:
## ---------------------------
## normexam
## -----------------------------------------------
## standlrt 0.591***
## (0.013)
##
## girlgirl 0.133***
## (0.034)
##
## boys_sch 0.183***
## (0.043)
##
## girls_sch 0.168***
## (0.033)
##
## Constant -0.161***
## (0.024)
##
## -----------------------------------------------
## Observations 4,059
## R2 0.364
## Adjusted R2 0.363
## Residual Std. Error 0.797 (df = 4054)
## F Statistic 580.148*** (df = 4; 4054)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
FULL Example from SURVEY.dat
library(userfriendlyscience)
library(ppcor)
library(olsrr)
##
## Attaching package: 'olsrr'
## The following object is masked from 'package:MASS':
##
## cement
## The following object is masked from 'package:datasets':
##
## rivers
#We are using a .dat file (survey.dat) created from the SPSS file survey.sav taken from SPSS Survival Manual 6th Edition Julie Pallant
#http://spss.allenandunwin.com.s3-website-ap-southeast-2.amazonaws.com/data-files.html#.Wb0vvnWP-po
#Results on a survey on well being
#We need to load the file so that we can use it in R.
sdata <- read.table("survey.dat")
#Setting the column names to be that used in the dataset
colnames(sdata) <- tolower(colnames(sdata))
#Look first at partial correlation
#First fiter out variables of interest and filter out na
myvars <- c("tpcoiss", "tpstress", "toptim", "tmarlow")
ydata <-na.omit(sdata[myvars])
#perception of control and stress controlling for social desirability
ppcor::spcor.test(ydata$tpcoiss, ydata$tpstress, ydata$tmarlow)
## estimate p.value statistic n gp Method
## 1 -0.5269534 1.862222e-31 -12.69154 422 1 pearson
#perception of control and optimism controlling for social desirability
ppcor::spcor.test(ydata$tpcoiss, ydata$toptim, ydata$tmarlow)
## estimate p.value statistic n gp Method
## 1 0.4830465 5.348979e-26 11.29257 422 1 pearson
#stress and optimism controlling for social desirability
ppcor::spcor.test(ydata$tpstress, ydata$toptim, ydata$tmarlow)
## estimate p.value statistic n gp Method
## 1 -0.4412444 1.73877e-21 -10.06483 422 1 pearson
#Get zero order correlations as well to fully explore the effect
cor.test(ydata$tpcoiss, ydata$tpstress)
##
## Pearson's product-moment correlation
##
## data: ydata$tpcoiss and ydata$tpstress
## t = -14.639, df = 420, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.6411275 -0.5143192
## sample estimates:
## cor
## -0.5812413
cor.test(ydata$tpcoiss, ydata$toptim)
##
## Pearson's product-moment correlation
##
## data: ydata$tpcoiss and ydata$toptim
## t = 12.351, df = 420, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4425181 0.5829097
## sample estimates:
## cor
## 0.5161727
cor.test(ydata$tpstress, ydata$toptim)
##
## Pearson's product-moment correlation
##
## data: ydata$tpstress and ydata$toptim
## t = -10.816, df = 420, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5382333 -0.3886119
## sample estimates:
## cor
## -0.4667559
#Look at differences in scores for gender
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(tpstress ~ sex, data=sdata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 1.9363 0.1648
## 431
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(tpstress~sex,var.equal=FALSE,data=sdata)#Variances are not equal
##
## Welch Two Sample t-test
##
## data: tpstress by sex
## t = 2.948, df = 415.89, p-value = 0.003379
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.5443502 2.7229363
## sample estimates:
## mean in group FEMALES mean in group MALES
## 27.42169 25.78804
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(tpcoiss ~ sex, data=sdata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 2.6386 0.105
## 428
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(tpcoiss~sex,var.equal=FALSE,data=sdata)
##
## Welch Two Sample t-test
##
## data: tpcoiss by sex
## t = -2.0357, df = 410.38, p-value = 0.04243
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -4.59066957 -0.08019182
## sample estimates:
## mean in group FEMALES mean in group MALES
## 59.63710 61.97253
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(toptim ~ sex, data=sdata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 4.2058 0.04089 *
## 433
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(toptim~sex,var.equal=TRUE,data=sdata)
##
## Two Sample t-test
##
## data: toptim by sex
## t = 0.42849, df = 433, p-value = 0.6685
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.6612571 1.0299563
## sample estimates:
## mean in group FEMALES mean in group MALES
## 22.19522 22.01087
#Conduct Levene's test for homogeneity of variance in library car
leveneTest(tmarlow ~ sex, data=sdata)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.0132 0.9087
## 431
#Conduct the t-test
#You can use the var.equal = TRUE option to specify equal variances and a pooled variance estimate
t.test(tmarlow~sex,var.equal=FALSE,data=sdata)
##
## Welch Two Sample t-test
##
## data: tmarlow by sex
## t = 2.2975, df = 398.33, p-value = 0.02211
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.06526408 0.83930423
## sample estimates:
## mean in group FEMALES mean in group MALES
## 5.496000 5.043716
#install the library userfriendlyscience and load it using the library command
#it has a really nice one-way anova function that provides
#nice summary output
#run a one-way anova test using the correct post-hoc test Tukey in our case
#Use Games-Howell for unequal variances
one.way <- oneway(sdata$agegp3, y = sdata$toptim, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=toptim and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [0; .05], point estimate = .02
## Eta Squared: 95% CI = [0; .05], point estimate = .02
##
## SS Df MS F p
## Between groups (error + effect) 179.07 2 89.53 4.64 .01
## Within groups (error only) 8333.95 432 19.29
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 0.74 -0.45 1.94 .308
## 45+-18 - 29 1.6 0.36 2.83 .007
## 45+-30 - 44 0.85 -0.37 2.07 .230
one.way <- oneway(sdata$agegp3, y = sdata$tpstress, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=tpstress and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [NA; .03], point estimate = .01
## Eta Squared: 95% CI = [0; .03], point estimate = .01
##
## SS Df MS F p
## Between groups (error + effect) 159.95 2 79.97 2.35 .096
## Within groups (error only) 14611.9 430 33.98
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 -0.99 -2.58 0.59 .307
## 45+-18 - 29 -1.47 -3.11 0.17 .088
## 45+-30 - 44 -0.48 -2.1 1.14 .767
one.way <- oneway(sdata$agegp3, y = sdata$tpcoiss, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=tpcoiss and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [.01; .08], point estimate = .04
## Eta Squared: 95% CI = [.01; .07], point estimate = .04
##
## SS Df MS F p
## Between groups (error + effect) 2565.21 2 1282.6 9.27 <.001
## Within groups (error only) 59057.51 427 138.31
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 1.1 -2.11 4.31 .698
## 45+-18 - 29 5.75 2.44 9.07 <.001
## 45+-30 - 44 4.65 1.36 7.94 .003
one.way <- oneway(sdata$agegp3, y = sdata$tmarlow, posthoc = 'Tukey')
#printout a summary of the anova
one.way
## ### Oneway Anova for y=tmarlow and x=agegp3 (groups: 18 - 29, 30 - 44, 45+)
##
## Omega squared: 95% CI = [.02; .1], point estimate = .05
## Eta Squared: 95% CI = [.03; .09], point estimate = .06
##
## SS Df MS F p
## Between groups (error + effect) 104.08 2 52.04 13.18 <.001
## Within groups (error only) 1697.68 430 3.95
##
##
## ### Post hoc test: Tukey
##
## diff lwr upr p adj
## 30 - 44-18 - 29 0.82 0.28 1.36 .001
## 45+-18 - 29 1.18 0.62 1.74 <.001
## 45+-30 - 44 0.36 -0.19 0.92 .278
Build the linear regression models
#Baseline model optimism and social desirability as predictors
model1=lm(sdata$tpcoiss~sdata$toptim+sdata$tmarlow)
stargazer(model1, type="text")
##
## ===============================================
## Dependent variable:
## ---------------------------
## tpcoiss
## -----------------------------------------------
## toptim 1.321***
## (0.111)
##
## tmarlow 1.390***
## (0.240)
##
## Constant 23.957***
## (2.655)
##
## -----------------------------------------------
## Observations 425
## R2 0.319
## Adjusted R2 0.315
## Residual Std. Error 9.936 (df = 422)
## F Statistic 98.673*** (df = 2; 422)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
#Check assumptions
#Cooks distance
cooks.distance(model1)
## 1 2 3 4 5
## 6.502551e-04 3.112103e-03 5.021039e-03 7.497759e-06 9.267960e-04
## 6 7 8 9 10
## 2.129260e-02 2.052856e-02 1.188297e-02 1.936683e-02 3.358488e-02
## 11 12 13 14 15
## 2.139564e-02 1.556123e-02 4.398459e-08 1.265492e-02 2.582840e-03
## 16 17 18 19 20
## 4.616937e-03 5.149222e-03 8.840492e-04 5.011005e-03 8.952237e-04
## 21 22 23 24 25
## 5.370918e-04 7.913716e-03 8.967520e-04 6.685494e-04 2.127960e-03
## 26 27 28 29 31
## 6.969384e-04 4.119936e-03 1.448822e-04 5.258085e-04 1.213924e-03
## 32 33 34 35 36
## 5.812128e-02 2.065601e-04 4.663671e-05 7.460092e-05 1.917659e-03
## 37 38 39 42 43
## 5.941958e-04 1.126810e-03 8.840492e-04 2.872576e-04 8.685130e-03
## 44 46 47 48 49
## 2.495491e-03 4.142058e-03 1.565434e-03 3.177883e-04 2.223772e-03
## 50 51 52 53 54
## 2.437659e-04 8.724413e-06 6.061452e-05 2.950526e-04 4.257250e-03
## 55 56 57 59 60
## 7.840810e-03 8.067189e-03 2.847546e-04 1.635709e-04 2.747022e-03
## 61 62 63 64 65
## 2.920793e-05 7.320939e-03 1.208383e-03 2.430978e-04 1.935852e-02
## 66 67 68 69 70
## 8.151233e-03 2.534092e-02 2.790511e-05 3.471963e-03 5.545158e-04
## 71 72 73 74 75
## 3.064099e-03 1.223719e-04 3.052052e-04 4.288045e-04 1.157374e-03
## 76 77 78 79 80
## 1.146592e-03 6.574317e-06 6.059503e-03 4.131341e-03 6.094302e-04
## 81 82 83 84 85
## 1.861582e-02 2.950526e-04 2.861795e-04 6.228444e-04 2.369347e-03
## 86 87 88 89 90
## 9.587631e-04 6.805413e-04 1.008620e-03 9.772701e-05 3.221221e-04
## 91 92 93 94 95
## 1.706153e-03 5.989866e-07 6.883234e-03 8.987336e-04 1.643000e-04
## 96 97 98 99 100
## 1.401412e-03 4.021454e-03 6.773808e-04 7.071666e-03 8.538847e-05
## 101 102 103 104 105
## 6.633850e-05 4.303473e-05 3.432661e-03 3.205774e-05 2.107019e-04
## 106 107 108 109 110
## 1.388027e-03 1.334037e-03 2.148214e-05 2.590986e-03 1.159461e-06
## 111 112 113 114 115
## 1.915811e-03 1.055125e-02 8.593910e-05 3.606825e-03 5.904843e-05
## 116 117 118 119 120
## 3.012951e-05 5.258085e-04 3.086994e-04 8.476463e-03 2.919163e-03
## 121 122 123 124 125
## 1.182984e-03 2.909403e-04 1.661236e-03 1.653797e-03 3.549001e-05
## 126 127 128 129 130
## 2.078038e-03 4.854594e-03 5.918968e-03 1.758888e-05 1.237878e-04
## 131 132 133 134 135
## 1.431355e-04 4.752285e-05 2.245079e-03 1.004769e-04 1.383757e-03
## 136 137 138 139 140
## 1.512817e-03 2.223728e-04 4.689399e-03 5.163570e-03 1.636156e-03
## 141 142 143 144 145
## 1.653905e-04 1.176677e-04 3.562349e-03 4.054783e-04 3.168772e-04
## 146 147 148 149 150
## 3.739763e-05 4.834626e-03 2.730971e-03 1.504892e-04 5.389321e-05
## 151 152 153 154 155
## 2.849946e-03 9.859851e-03 4.908827e-03 7.524588e-04 1.000702e-04
## 156 157 158 159 160
## 4.056763e-03 3.128635e-05 1.818171e-04 6.867160e-04 4.148999e-04
## 161 162 163 164 165
## 3.486215e-03 1.833956e-06 1.341793e-06 3.890415e-04 1.516071e-06
## 166 167 168 169 170
## 1.086401e-03 1.386825e-04 3.362393e-04 2.146705e-03 1.169215e-03
## 171 172 173 174 175
## 6.293545e-03 9.833695e-05 7.656084e-04 2.045181e-03 1.557336e-04
## 177 178 179 180 181
## 1.176677e-04 4.912000e-03 1.372747e-03 4.663926e-03 2.440071e-03
## 182 183 184 185 186
## 5.105591e-03 3.332627e-03 4.475102e-07 6.368963e-03 1.129802e-02
## 187 188 189 190 191
## 5.618535e-03 6.857586e-03 8.870892e-05 4.529661e-04 1.191831e-03
## 192 193 194 195 196
## 1.151615e-03 1.347641e-03 2.624262e-03 3.634924e-06 1.079861e-04
## 197 198 199 200 201
## 5.948127e-03 1.112197e-05 2.372697e-05 3.178253e-04 5.271255e-07
## 202 203 204 205 206
## 3.113456e-04 3.630448e-04 6.366351e-06 7.214455e-04 5.364698e-05
## 207 208 209 210 211
## 1.637006e-04 5.814801e-04 2.003193e-04 7.434163e-04 4.665976e-04
## 212 213 214 215 216
## 4.529661e-04 1.912934e-02 6.091161e-06 1.174969e-03 3.539114e-04
## 217 218 219 220 221
## 1.790964e-07 2.563216e-03 1.443522e-03 5.311477e-04 6.090387e-03
## 222 223 224 225 226
## 1.935501e-04 2.090523e-04 3.372219e-04 2.496893e-03 3.246253e-04
## 227 228 229 230 231
## 9.461922e-05 1.033185e-03 2.035038e-03 1.632791e-03 1.727713e-04
## 232 233 234 235 236
## 2.373647e-04 1.418739e-05 5.545845e-04 2.420401e-05 3.935649e-03
## 237 238 239 240 241
## 3.402395e-03 7.944575e-03 7.434163e-04 3.730773e-06 4.906488e-05
## 242 243 244 245 246
## 1.092527e-04 1.522640e-03 2.044247e-08 7.820040e-04 3.991612e-04
## 247 248 249 250 251
## 4.265360e-03 1.169998e-03 2.593052e-02 5.204159e-03 5.015126e-03
## 252 253 254 255 256
## 2.878781e-03 9.133392e-03 3.900505e-04 1.266901e-03 7.177777e-07
## 257 258 259 260 261
## 8.111183e-04 1.659941e-03 7.276857e-05 4.032221e-05 1.090452e-04
## 262 263 264 265 266
## 6.152156e-04 3.386712e-04 4.906488e-05 1.768346e-04 3.641208e-04
## 267 268 269 270 271
## 8.293862e-05 2.931371e-03 7.562122e-03 1.113867e-03 1.285775e-04
## 272 273 274 275 276
## 5.369362e-05 2.221514e-03 4.393732e-03 1.836714e-03 1.634673e-02
## 277 279 280 281 282
## 6.571886e-03 2.525762e-05 1.959567e-03 1.031952e-04 1.108088e-03
## 283 284 285 286 287
## 8.621910e-03 6.258353e-05 7.033311e-03 2.961425e-03 3.310413e-04
## 288 289 290 291 292
## 1.386825e-04 4.275273e-03 9.090313e-06 1.626155e-03 2.061272e-04
## 293 294 295 296 297
## 5.398414e-04 7.038954e-04 1.429454e-03 2.808139e-04 1.224816e-03
## 299 300 301 302 303
## 1.274288e-03 2.273996e-03 2.670829e-02 1.468360e-03 4.146889e-04
## 304 305 306 307 308
## 3.048287e-03 4.545388e-04 9.658637e-06 4.392073e-07 7.495529e-03
## 309 310 311 312 313
## 2.537379e-03 1.627368e-03 6.517757e-06 1.993385e-05 2.726138e-03
## 314 315 316 317 318
## 4.312277e-04 1.750999e-03 2.343291e-03 2.851173e-03 4.896752e-06
## 319 320 321 322 323
## 9.058775e-04 1.718906e-03 1.414605e-03 9.822144e-04 1.569802e-05
## 324 325 326 327 328
## 1.013187e-04 1.396138e-05 3.012951e-05 4.506207e-04 5.449837e-04
## 329 330 331 332 333
## 1.808162e-03 1.876406e-05 2.909403e-04 8.809182e-05 6.565543e-04
## 334 335 336 337 338
## 7.727485e-03 2.837468e-05 1.191831e-03 3.445230e-03 1.675114e-03
## 339 340 341 343 344
## 7.785885e-04 9.405542e-04 6.633704e-05 6.535943e-05 1.524739e-04
## 345 346 347 348 349
## 4.702745e-05 8.737387e-04 3.838936e-04 1.643000e-04 7.908824e-03
## 350 351 352 353 354
## 6.094620e-04 8.032567e-04 2.426273e-03 2.333935e-03 2.071698e-03
## 355 356 357 358 359
## 1.708213e-04 2.658016e-03 1.591899e-04 2.593234e-03 1.108950e-04
## 360 361 362 363 364
## 3.177883e-04 1.117259e-04 1.822081e-04 6.380893e-04 8.912493e-03
## 365 366 367 368 369
## 7.786145e-04 8.311506e-04 9.999980e-05 7.911521e-07 1.493234e-03
## 370 371 372 373 374
## 5.435634e-04 6.325072e-03 3.977681e-03 1.097875e-03 1.641530e-03
## 375 376 377 378 379
## 1.502801e-02 1.600365e-05 1.049424e-03 1.725883e-04 2.748855e-03
## 380 381 382 383 384
## 1.476490e-03 3.220789e-04 8.402395e-06 3.164926e-03 3.142905e-03
## 385 386 387 388 389
## 3.635277e-04 1.445644e-03 6.621007e-04 1.095440e-06 1.816590e-04
## 390 391 392 394 395
## 3.254265e-03 8.134463e-06 4.347713e-03 7.918642e-04 4.906216e-05
## 396 397 398 399 400
## 1.290782e-02 1.547347e-03 4.808448e-04 1.557004e-03 6.464571e-05
## 401 402 403 404 405
## 1.250092e-04 7.507327e-05 1.879441e-03 1.004769e-04 1.455795e-03
## 406 407 408 409 410
## 3.797437e-06 5.038075e-05 2.543321e-03 2.373799e-03 3.341059e-05
## 411 412 413 414 415
## 5.051268e-04 4.228503e-05 7.195078e-05 8.468835e-03 2.917434e-03
## 416 417 418 419 420
## 5.706427e-04 7.472142e-07 1.395971e-03 1.052911e-02 1.448435e-03
## 421 423 424 425 426
## 4.238825e-05 1.753710e-02 1.241284e-03 3.439611e-04 1.070199e-06
## 427 428 429 430 431
## 1.040129e-04 3.523737e-04 3.010825e-04 4.666765e-04 7.559538e-04
## 432 433 435 437 439
## 4.752285e-05 4.500997e-03 2.245644e-03 4.560286e-05 4.375925e-03
#Plot Cooks distance
plot(cooks.distance(model1), ylab="Cook's statistic")
#Create histogram
#A density plot of the residuals
plot(density(resid(model1)))
#Create a QQ plotqqPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model1) # leverage plots
#Collinearity
vifmodel<-vif(model1)
#Calculate tolerance
1/vifmodel
## sdata$toptim sdata$tmarlow
## 0.9836225 0.9836225
#Second model adding in stress
model2=lm(sdata$tpcoiss~sdata$toptim+sdata$tmarlow+sdata$tpstress)
summary(model2)
##
## Call:
## lm(formula = sdata$tpcoiss ~ sdata$toptim + sdata$tmarlow + sdata$tpstress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.253 -5.034 0.271 5.701 28.070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 58.55471 4.40587 13.290 < 2e-16 ***
## sdata$toptim 0.84267 0.11264 7.481 4.38e-13 ***
## sdata$tmarlow 0.98044 0.22400 4.377 1.52e-05 ***
## sdata$tpstress -0.81767 0.08663 -9.438 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.019 on 418 degrees of freedom
## (17 observations deleted due to missingness)
## Multiple R-squared: 0.4402, Adjusted R-squared: 0.4361
## F-statistic: 109.5 on 3 and 418 DF, p-value: < 2.2e-16
#Check assumptions
#Cooks distance
cooks.distance(model2)
## 1 2 3 4 5
## 4.386133e-04 1.122128e-02 1.841839e-02 8.104241e-04 1.677983e-03
## 6 7 8 9 10
## 3.951943e-02 1.278646e-02 1.858489e-02 1.124209e-02 1.319163e-02
## 11 12 13 14 15
## 2.095067e-02 3.536274e-02 2.078877e-04 1.510310e-02 4.006136e-04
## 16 17 18 19 20
## 2.818643e-03 5.081900e-03 2.784382e-02 6.187649e-04 9.385656e-04
## 21 22 23 24 25
## 1.692352e-04 2.913993e-02 2.425825e-03 1.963788e-03 1.334735e-03
## 26 27 28 29 31
## 2.386220e-05 5.446850e-03 1.513688e-03 9.679650e-07 3.836379e-04
## 32 33 34 35 36
## 3.596554e-02 6.542349e-04 1.963583e-04 4.635160e-04 1.006445e-03
## 37 38 39 42 43
## 3.779544e-04 6.207859e-04 2.893225e-03 1.518792e-03 6.252466e-03
## 44 46 47 48 49
## 4.803713e-04 3.623659e-03 1.038313e-02 2.437726e-03 5.997050e-04
## 50 51 52 53 54
## 6.230510e-03 1.268997e-04 1.895822e-03 1.023493e-03 5.358517e-03
## 55 56 57 59 60
## 6.697990e-02 4.617651e-02 7.650889e-04 4.571700e-03 3.066488e-03
## 61 62 63 64 65
## 3.898795e-04 6.702801e-03 9.716547e-04 8.870216e-05 7.531584e-03
## 66 67 68 69 70
## 1.070167e-02 1.516978e-02 5.397230e-05 4.659988e-04 8.643770e-03
## 71 72 73 74 75
## 1.326955e-03 4.032575e-03 7.038843e-04 6.651905e-04 3.143702e-04
## 76 77 78 79 80
## 4.152421e-04 1.621811e-05 7.732975e-04 1.689876e-02 1.567265e-05
## 81 82 83 84 85
## 1.402302e-02 6.050244e-04 3.492398e-04 5.618475e-04 1.600254e-03
## 86 87 88 89 90
## 3.831070e-06 3.579970e-04 3.061522e-04 1.108126e-03 1.156157e-03
## 91 92 93 94 95
## 1.376175e-03 3.209951e-04 3.646189e-03 2.361536e-04 3.462976e-04
## 96 97 98 99 100
## 8.202307e-05 1.680604e-04 7.306675e-04 4.747362e-03 7.856356e-05
## 101 102 103 104 105
## 1.008669e-05 6.809411e-04 1.238707e-02 2.383199e-04 6.062445e-04
## 106 107 108 109 110
## 1.233405e-03 8.383219e-04 2.944082e-04 4.329760e-04 1.011100e-03
## 111 112 113 114 115
## 1.938113e-03 7.450220e-03 1.025415e-04 2.037185e-03 1.223689e-04
## 116 117 118 119 120
## 5.507892e-06 3.817765e-04 3.338964e-05 7.695163e-03 2.624638e-03
## 121 122 123 124 125
## 9.518047e-04 6.441381e-05 1.690502e-03 1.098883e-03 6.995576e-04
## 126 127 128 129 130
## 5.990789e-03 1.280055e-02 3.799758e-03 6.759402e-05 6.630600e-05
## 131 132 133 134 135
## 2.479354e-04 3.051437e-05 5.508596e-04 1.585305e-04 1.050701e-03
## 136 137 138 139 140
## 7.095943e-04 8.935817e-04 6.350803e-04 4.076625e-02 1.429977e-02
## 141 142 143 144 145
## 1.206158e-03 5.763347e-04 2.135666e-03 8.705416e-09 1.884086e-03
## 146 147 148 149 150
## 4.320267e-05 3.078351e-03 2.194644e-03 1.164725e-05 6.621026e-05
## 151 152 153 154 155
## 1.402424e-02 6.955861e-03 3.331298e-03 1.002329e-03 1.530437e-04
## 156 157 158 159 160
## 2.578946e-03 7.411840e-06 4.302432e-04 3.132903e-03 5.284563e-05
## 161 162 163 164 165
## 1.908219e-03 1.067378e-03 5.755838e-04 6.092257e-04 5.196341e-05
## 166 167 168 169 170
## 8.455585e-04 3.543527e-04 1.318425e-04 1.881276e-03 9.157110e-04
## 171 172 173 174 175
## 6.946290e-03 5.300279e-05 2.127500e-05 1.295259e-03 7.237538e-05
## 177 178 179 180 181
## 8.855640e-05 4.740295e-03 1.064043e-03 3.319243e-03 3.817172e-04
## 182 183 184 185 186
## 4.436219e-03 2.669174e-03 9.347653e-04 6.462383e-03 1.053434e-02
## 187 188 189 190 191
## 5.679416e-03 4.930282e-03 4.027091e-04 4.504617e-04 1.643329e-03
## 192 193 194 195 196
## 4.818361e-05 1.592021e-03 2.571586e-03 4.890655e-05 2.127256e-03
## 197 198 199 200 201
## 6.103995e-03 1.201321e-04 1.864803e-04 6.200510e-05 1.986242e-04
## 202 203 204 205 206
## 2.126468e-04 1.579025e-05 2.576602e-05 2.475584e-04 1.012185e-04
## 207 208 209 210 211
## 8.324393e-05 1.107312e-03 3.054095e-07 2.217814e-04 4.681305e-04
## 212 213 214 215 216
## 1.115400e-03 1.223851e-02 5.757810e-06 4.472341e-04 8.394730e-04
## 217 218 219 220 221
## 9.312336e-06 3.066385e-03 4.856027e-04 5.113950e-04 4.688919e-03
## 222 223 224 225 226
## 8.904989e-04 2.971711e-04 1.265362e-04 2.381366e-03 4.750834e-06
## 227 228 229 230 231
## 2.481636e-04 1.304818e-04 1.020656e-03 1.199490e-02 2.910689e-04
## 232 233 234 235 236
## 1.204419e-04 7.463380e-06 7.239221e-04 1.370971e-05 3.586538e-03
## 237 238 239 240 241
## 1.352064e-03 7.742845e-03 3.192741e-05 9.414624e-06 1.400134e-05
## 242 243 244 245 246
## 2.247768e-04 2.751394e-03 4.638816e-06 1.092434e-03 4.336220e-05
## 247 248 249 250 251
## 5.012996e-03 1.846043e-03 2.276583e-02 3.502830e-03 3.373733e-03
## 252 253 254 255 256
## 1.637806e-03 7.437340e-03 6.446441e-05 1.249926e-03 1.628093e-05
## 257 258 259 260 261
## 2.089036e-03 8.269490e-04 6.272452e-04 1.555396e-04 5.870607e-05
## 262 263 264 265 266
## 1.277570e-03 8.920941e-05 1.653760e-03 5.820557e-06 2.716542e-04
## 267 268 269 270 271
## 2.781698e-05 2.372743e-03 7.082099e-03 9.568469e-04 5.097000e-06
## 272 273 274 275 276
## 2.253401e-04 1.783613e-03 3.420871e-03 1.023987e-03 9.543107e-03
## 277 279 280 281 282
## 8.586335e-03 1.260799e-05 4.736527e-03 1.722811e-07 5.328438e-05
## 283 284 285 286 287
## 9.064871e-03 2.146134e-05 5.317210e-03 1.760873e-03 1.905966e-05
## 288 289 290 291 292
## 4.640265e-05 4.380822e-03 1.093820e-04 9.877358e-04 1.344988e-04
## 293 294 295 296 297
## 1.585704e-04 3.916155e-04 7.051611e-04 1.610758e-04 4.548479e-04
## 299 300 301 302 303
## 4.538674e-04 1.201836e-03 2.143479e-02 1.205541e-03 3.031590e-04
## 304 305 306 307 308
## 8.962552e-04 1.114583e-04 1.393493e-04 5.159693e-06 6.983783e-03
## 309 310 311 312 313
## 2.251318e-03 2.902743e-03 2.288025e-04 6.227432e-04 2.346624e-03
## 314 315 316 317 318
## 4.089628e-05 1.387249e-03 2.760761e-03 2.495428e-03 3.530648e-05
## 319 320 321 322 323
## 3.380011e-04 5.835935e-04 2.496055e-03 2.774031e-04 2.308443e-04
## 324 325 326 327 328
## 1.686315e-04 1.143373e-03 9.677548e-05 1.683532e-03 7.132650e-04
## 329 330 331 332 333
## 1.353526e-03 5.250248e-06 1.256242e-04 7.959785e-05 4.593538e-04
## 334 335 336 337 338
## 5.517579e-03 1.932397e-05 5.013628e-04 3.298492e-03 6.990907e-04
## 339 340 341 343 344
## 4.655428e-05 3.522176e-04 2.364236e-05 2.207084e-05 3.881046e-05
## 345 346 347 348 349
## 1.627580e-05 1.514174e-03 1.055266e-04 1.433574e-04 6.123495e-03
## 350 351 352 353 354
## 2.574264e-04 3.304918e-04 6.589807e-04 8.551661e-04 1.323455e-03
## 355 356 357 358 359
## 5.606057e-06 2.238127e-03 5.255332e-05 1.280023e-03 1.999500e-05
## 360 361 362 363 364
## 5.766521e-05 6.914136e-05 6.995432e-05 6.633236e-04 2.361188e-02
## 365 366 367 368 369
## 4.722831e-04 5.031333e-03 2.895058e-04 1.072320e-04 1.141158e-03
## 370 371 372 373 374
## 4.935098e-04 4.322763e-03 4.292238e-03 5.731036e-04 1.015266e-03
## 375 376 377 378 379
## 1.222428e-02 4.520365e-04 8.836257e-04 4.301008e-06 1.025994e-03
## 380 381 382 383 384
## 1.155738e-03 7.250348e-05 6.368504e-04 2.767466e-03 2.247564e-03
## 385 386 387 388 389
## 1.409342e-04 8.629613e-05 3.288017e-06 1.437695e-05 1.175090e-06
## 390 391 392 394 395
## 2.532978e-03 7.736559e-05 4.522563e-03 9.199994e-04 1.636145e-09
## 396 397 398 399 400
## 9.179859e-03 1.939028e-03 1.048373e-03 2.006180e-03 9.043328e-05
## 401 402 403 404 405
## 2.043244e-04 1.819969e-04 5.282918e-03 1.047493e-05 3.865099e-04
## 406 407 408 409 410
## 1.595736e-04 9.715567e-07 1.649315e-03 4.660351e-04 2.702553e-06
## 411 412 413 414 415
## 3.265448e-04 2.975850e-05 1.782046e-04 6.869838e-03 1.578350e-03
## 416 417 418 419 420
## 1.320362e-03 6.239612e-05 3.516138e-03 6.107803e-03 5.268216e-03
## 421 423 424 425 426
## 8.229372e-06 1.461833e-02 9.274811e-04 1.289364e-05 2.072355e-05
## 427 428 429 430 431
## 2.455461e-05 3.639891e-04 2.562616e-04 2.381704e-04 5.211356e-04
## 432 437
## 3.704604e-04 1.143229e-03
#Create histogram
#A density plot of the residuals
plot(density(resid(model2)))
#Create a QQ plot qPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model2) # leverage plots
#Collinearity
vif(model2)
## sdata$toptim sdata$tmarlow sdata$tpstress
## 1.279007 1.057358 1.330851
sqrt(vif(model2))
## sdata$toptim sdata$tmarlow sdata$tpstress
## 1.130932 1.028279 1.153625
#Model 3 adding in gender
#dummycode
sdata$gender=recode(sdata$sex,'0=1;1=2')
model3=lm(sdata$tpcoiss~sdata$toptim+sdata$tmarlow+sdata$tpstress+sdata$sex)
summary(model3)
##
## Call:
## lm(formula = sdata$tpcoiss ~ sdata$toptim + sdata$tmarlow + sdata$tpstress +
## sdata$sex)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.785 -5.241 0.139 5.801 28.424
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56.17192 4.56967 12.292 < 2e-16 ***
## sdata$toptim 0.86391 0.11285 7.655 1.36e-13 ***
## sdata$tmarlow 1.03612 0.22525 4.600 5.62e-06 ***
## sdata$tpstress -0.78439 0.08814 -8.899 < 2e-16 ***
## sdata$sexMALES 1.71591 0.90775 1.890 0.0594 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.991 on 417 degrees of freedom
## (17 observations deleted due to missingness)
## Multiple R-squared: 0.4449, Adjusted R-squared: 0.4396
## F-statistic: 83.56 on 4 and 417 DF, p-value: < 2.2e-16
plot(model3)
#Check assumptions
#Cooks distance
cooks.distance(model3)
## 1 2 3 4 5
## 4.197679e-04 1.211857e-02 1.618401e-02 5.551629e-04 2.264980e-03
## 6 7 8 9 10
## 3.231304e-02 9.922411e-03 2.344161e-02 8.680495e-03 1.496076e-02
## 11 12 13 14 15
## 2.101761e-02 3.420758e-02 9.772502e-05 1.183614e-02 2.118482e-04
## 16 17 18 19 20
## 2.169598e-03 3.911430e-03 2.351318e-02 3.793327e-04 8.606866e-04
## 21 22 23 24 25
## 2.142289e-05 2.556939e-02 2.569283e-03 2.011169e-03 1.843008e-03
## 26 27 28 29 31
## 3.790730e-06 4.373871e-03 1.705208e-03 6.581347e-06 8.048003e-04
## 32 33 34 35 36
## 2.820298e-02 7.733624e-04 8.887682e-05 3.814116e-04 1.321204e-03
## 37 38 39 42 43
## 3.742400e-04 8.454544e-04 3.412412e-03 9.610690e-04 4.561408e-03
## 44 46 47 48 49
## 3.149815e-04 2.948345e-03 9.000356e-03 1.945060e-03 3.657561e-04
## 50 51 52 53 54
## 5.664595e-03 2.798421e-04 1.735660e-03 6.136839e-04 5.376345e-03
## 55 56 57 59 60
## 5.875351e-02 4.307659e-02 8.650980e-04 4.020425e-03 2.287152e-03
## 61 62 63 64 65
## 2.855970e-04 6.774712e-03 9.272567e-04 1.290323e-04 5.768160e-03
## 66 67 68 69 70
## 8.400061e-03 1.183437e-02 3.194868e-05 7.653155e-04 7.403000e-03
## 71 72 73 74 75
## 9.829533e-04 3.375666e-03 9.262198e-04 6.846940e-04 7.718024e-04
## 76 77 78 79 80
## 2.564665e-04 4.014454e-07 6.411572e-04 1.537949e-02 1.245155e-06
## 81 82 83 84 85
## 1.015045e-02 7.780475e-04 3.362903e-04 8.177173e-04 2.374995e-03
## 86 87 88 89 90
## 3.319909e-05 7.542612e-04 1.770498e-04 1.066118e-03 1.332752e-03
## 91 92 93 94 95
## 1.432210e-03 1.959148e-04 4.195844e-03 6.321568e-04 5.037242e-04
## 96 97 98 99 100
## 2.854249e-05 2.739247e-05 8.179369e-04 7.255416e-03 1.756023e-04
## 101 102 103 104 105
## 3.001939e-05 7.345742e-04 1.164994e-02 4.180816e-04 8.294681e-04
## 106 107 108 109 110
## 1.951387e-03 1.144373e-03 4.222578e-04 2.941887e-04 1.290234e-03
## 111 112 113 114 115
## 2.272432e-03 8.906600e-03 3.313974e-05 2.603343e-03 1.867603e-04
## 116 117 118 119 120
## 6.797506e-06 6.601685e-04 1.803555e-07 6.741639e-03 3.422203e-03
## 121 122 123 124 125
## 1.503357e-03 1.788088e-05 2.180131e-03 1.285808e-03 9.625718e-04
## 126 127 128 129 130
## 4.953154e-03 1.233853e-02 2.830108e-03 1.493332e-05 1.607792e-06
## 131 132 133 134 135
## 1.364789e-04 1.130918e-04 3.546110e-04 1.718545e-04 1.339119e-03
## 136 137 138 139 140
## 1.268833e-03 1.004576e-03 3.598073e-04 3.457427e-02 1.177440e-02
## 141 142 143 144 145
## 1.465423e-03 6.586219e-04 1.692150e-03 5.728757e-06 1.557841e-03
## 146 147 148 149 150
## 1.118464e-05 3.838866e-03 3.106583e-03 8.568775e-05 3.553826e-05
## 151 152 153 154 155
## 1.246649e-02 8.086788e-03 2.643602e-03 1.456764e-03 3.460046e-04
## 156 157 158 159 160
## 1.996944e-03 1.239686e-06 5.470631e-04 2.295693e-03 2.132351e-05
## 161 162 163 164 165
## 1.518723e-03 7.688412e-04 3.637548e-04 4.600586e-04 1.630315e-05
## 166 167 168 169 170
## 9.387885e-04 3.109898e-04 2.811556e-05 2.696406e-03 1.006388e-03
## 171 172 173 174 175
## 6.305138e-03 1.826157e-05 1.139847e-04 9.890679e-04 4.622274e-05
## 177 178 179 180 181
## 5.052888e-05 4.211214e-03 2.027140e-03 2.798842e-03 6.994851e-04
## 182 183 184 185 186
## 6.132901e-03 3.532210e-03 6.137388e-04 7.337603e-03 8.815952e-03
## 187 188 189 190 191
## 5.383469e-03 5.982091e-03 2.209876e-04 5.225183e-04 1.736916e-03
## 192 193 194 195 196
## 1.868019e-04 1.227234e-03 2.975273e-03 9.202072e-05 2.526248e-03
## 197 198 199 200 201
## 4.980183e-03 1.872972e-04 1.115488e-04 1.887004e-04 7.764134e-05
## 202 203 204 205 206
## 4.584208e-04 7.579627e-05 5.554306e-06 1.657696e-04 1.571302e-04
## 207 208 209 210 211
## 1.887963e-04 1.178353e-03 8.196134e-06 1.292070e-04 6.988422e-04
## 212 213 214 215 216
## 1.836346e-03 9.680570e-03 3.959528e-07 8.244072e-04 8.892333e-04
## 217 218 219 220 221
## 8.193632e-07 3.196681e-03 3.262213e-04 6.803670e-04 3.960848e-03
## 222 223 224 225 226
## 7.875614e-04 4.034885e-04 9.144393e-05 2.000980e-03 1.580416e-06
## 227 228 229 230 231
## 1.251735e-04 4.853038e-05 8.364939e-04 1.050282e-02 4.277987e-04
## 232 233 234 235 236
## 3.209268e-04 2.685046e-05 1.229495e-03 1.239696e-06 3.214409e-03
## 237 238 239 240 241
## 9.698840e-04 1.182820e-02 1.021546e-04 5.277873e-07 1.127162e-04
## 242 243 244 245 246
## 1.881968e-04 2.164420e-03 4.245212e-07 1.509754e-03 1.964100e-04
## 247 248 249 250 251
## 6.573517e-03 1.950828e-03 2.166570e-02 3.045035e-03 3.120855e-03
## 252 253 254 255 256
## 1.417851e-03 9.999129e-03 2.069329e-05 2.226214e-03 4.527933e-06
## 257 258 259 260 261
## 3.130802e-03 6.585050e-04 6.513967e-04 1.986348e-04 4.878517e-06
## 262 263 264 265 266
## 1.114737e-03 2.094699e-05 1.568792e-03 1.800409e-05 4.649115e-04
## 267 268 269 270 271
## 1.585284e-06 1.964130e-03 5.910648e-03 1.432358e-03 2.332845e-08
## 272 273 274 275 276
## 4.030685e-04 2.754178e-03 3.626445e-03 9.083886e-04 1.011470e-02
## 277 279 280 281 282
## 8.473261e-03 3.585344e-05 4.637712e-03 9.694950e-06 1.749809e-04
## 283 284 285 286 287
## 8.280766e-03 6.874586e-05 4.168752e-03 2.036204e-03 7.963922e-05
## 288 289 290 291 292
## 3.215642e-06 3.875906e-03 1.643751e-04 9.433776e-04 8.932770e-05
## 293 294 295 296 297
## 9.516064e-05 2.844443e-04 4.194760e-04 1.148010e-04 7.885892e-04
## 299 300 301 302 303
## 1.053573e-03 2.040621e-03 1.746390e-02 1.459593e-03 6.959472e-04
## 304 305 306 307 308
## 5.881585e-04 2.134193e-04 2.817285e-04 6.740716e-05 6.774610e-03
## 309 310 311 312 313
## 3.136208e-03 2.552473e-03 1.167534e-04 5.114699e-04 2.411268e-03
## 314 315 316 317 318
## 1.010636e-04 1.428834e-03 2.352240e-03 3.147816e-03 5.248036e-06
## 319 320 321 322 323
## 1.550405e-04 7.489822e-04 2.098045e-03 5.707228e-04 4.662413e-04
## 324 325 326 327 328
## 2.157255e-04 1.327133e-03 1.356481e-04 1.638573e-03 5.604195e-04
## 329 330 331 332 333
## 1.285783e-03 5.643174e-07 2.122820e-04 1.265711e-04 4.761796e-04
## 334 335 336 337 338
## 5.093441e-03 1.105760e-06 3.573770e-04 4.116176e-03 4.816687e-04
## 339 340 341 343 344
## 5.366328e-06 5.590812e-04 1.630920e-06 2.778076e-06 1.104570e-04
## 345 346 347 348 349
## 1.016314e-04 1.449896e-03 5.954211e-05 1.012711e-04 4.983936e-03
## 350 351 352 353 354
## 1.939200e-04 2.196996e-04 1.171223e-03 5.847426e-04 1.630944e-03
## 355 356 357 358 359
## 8.677706e-08 2.287167e-03 2.132634e-05 2.309821e-03 2.387297e-06
## 360 361 362 363 364
## 1.733529e-04 4.974783e-05 2.299280e-04 8.510232e-04 2.006994e-02
## 365 366 367 368 369
## 4.177580e-04 5.147529e-03 5.117771e-04 2.998917e-04 1.351073e-03
## 370 371 372 373 374
## 6.899045e-04 5.228499e-03 4.600990e-03 4.669527e-04 8.438978e-04
## 375 376 377 378 379
## 1.628354e-02 7.624859e-04 8.018057e-04 4.777453e-06 1.873800e-03
## 380 381 382 383 384
## 1.819473e-03 1.832969e-04 4.039127e-04 3.244130e-03 1.685125e-03
## 385 386 387 388 389
## 1.025939e-04 3.137450e-05 2.509090e-05 9.521722e-05 3.301360e-06
## 390 391 392 394 395
## 2.001649e-03 1.905834e-05 6.323092e-03 1.292753e-03 8.664254e-06
## 396 397 398 399 400
## 7.407007e-03 2.359656e-03 1.803314e-03 2.069562e-03 4.253547e-05
## 401 402 403 404 405
## 1.136323e-04 1.140534e-04 4.975520e-03 4.496540e-05 2.558134e-04
## 406 407 408 409 410
## 1.133500e-04 1.842323e-05 2.351419e-03 8.634116e-04 2.216123e-05
## 411 412 413 414 415
## 4.282417e-04 6.879309e-06 4.223486e-04 5.942391e-03 1.266087e-03
## 416 417 418 419 420
## 1.072475e-03 9.572363e-06 3.647850e-03 4.771934e-03 4.535670e-03
## 421 423 424 425 426
## 3.759026e-05 1.471750e-02 1.470953e-03 3.668430e-05 5.600332e-05
## 427 428 429 430 431
## 9.061783e-05 3.107488e-04 1.358236e-04 4.546927e-04 6.059712e-04
## 432 437
## 5.939650e-04 1.150430e-03
#Create histogram
#A density plot of the residuals
plot(density(resid(model3)))
#Create a QQ plot qqPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model3) # leverage plots
#Collinearity
vif(model3)
## sdata$toptim sdata$tmarlow sdata$tpstress sdata$sex
## 1.291821 1.075754 1.386133 1.050668
sqrt(vif(model3))
## sdata$toptim sdata$tmarlow sdata$tpstress sdata$sex
## 1.136583 1.037185 1.177342 1.025021
#Model 4 adding in interaction term gender*stress
#create interaction term
sdata$intgenstress=as.numeric(sdata$gender)*sdata$tpstress
model4=lm(sdata$tpcoiss~sdata$toptim+sdata$tmarlow+sdata$tpstress+sdata$gender+sdata$intgenstress)
summary(model4)
##
## Call:
## lm(formula = sdata$tpcoiss ~ sdata$toptim + sdata$tmarlow + sdata$tpstress +
## sdata$gender + sdata$intgenstress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -35.275 -5.186 0.235 5.836 28.198
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 55.48477 4.86777 11.398 < 2e-16 ***
## sdata$toptim 0.86682 0.11318 7.659 1.33e-13 ***
## sdata$tmarlow 1.02637 0.22671 4.527 7.81e-06 ***
## sdata$tpstress -0.69471 0.23450 -2.962 0.00323 **
## sdata$genderMALES 3.42931 4.24948 0.807 0.42013
## sdata$intgenstress -0.06507 0.15766 -0.413 0.68000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9 on 416 degrees of freedom
## (17 observations deleted due to missingness)
## Multiple R-squared: 0.4451, Adjusted R-squared: 0.4385
## F-statistic: 66.75 on 5 and 416 DF, p-value: < 2.2e-16
plot(model4)
#Check assumptions
#Cooks distance
cooks.distance(model4)
## 1 2 3 4 5
## 3.683116e-04 1.178676e-02 1.644426e-02 5.921484e-04 1.911109e-03
## 6 7 8 9 10
## 3.002889e-02 1.058362e-02 3.269252e-02 1.089707e-02 2.645437e-02
## 11 12 13 14 15
## 1.950181e-02 3.899282e-02 2.062466e-04 1.560389e-02 1.749112e-04
## 16 17 18 19 20
## 2.178498e-03 4.778911e-03 2.797210e-02 6.712949e-04 7.054063e-04
## 21 22 23 24 25
## 1.207878e-04 2.932034e-02 2.164039e-03 1.732762e-03 1.776822e-03
## 26 27 28 29 31
## 8.438375e-06 5.174328e-03 1.477976e-03 1.689095e-05 6.693014e-04
## 32 33 34 35 36
## 2.870488e-02 1.367956e-03 7.293801e-05 3.527067e-04 1.119045e-03
## 37 38 39 42 43
## 3.316852e-04 7.061671e-04 4.842655e-03 1.009167e-03 5.502894e-03
## 44 46 47 48 49
## 3.682338e-04 3.127571e-03 8.421178e-03 3.146750e-03 4.488304e-04
## 50 51 52 53 54
## 6.177542e-03 2.151253e-04 1.680959e-03 6.133201e-04 4.631203e-03
## 55 56 57 59 60
## 1.001518e-01 7.167624e-02 7.277119e-04 3.383246e-03 2.016119e-03
## 61 62 63 64 65
## 2.350115e-04 5.663261e-03 7.809555e-04 1.041914e-04 5.772658e-03
## 66 67 68 69 70
## 8.643961e-03 1.290567e-02 3.897609e-05 1.109233e-03 6.436888e-03
## 71 72 73 74 75
## 8.623124e-04 3.626219e-03 7.881128e-04 8.903274e-04 7.153656e-04
## 76 77 78 79 80
## 2.233232e-04 2.984345e-08 4.815933e-04 1.510601e-02 5.630290e-06
## 81 82 83 84 85
## 1.047456e-02 1.711374e-03 2.787357e-04 7.954411e-04 2.579801e-03
## 86 87 88 89 90
## 1.089499e-04 7.386730e-04 1.983170e-04 1.420885e-03 1.129245e-03
## 91 92 93 94 95
## 1.195295e-03 2.300407e-04 5.443813e-03 6.965125e-04 9.945682e-04
## 96 97 98 99 100
## 4.931185e-05 5.330733e-06 7.924720e-04 8.064176e-03 2.843402e-04
## 101 102 103 104 105
## 2.403436e-05 7.286398e-04 1.084999e-02 4.658209e-04 7.429898e-04
## 106 107 108 109 110
## 1.828286e-03 1.203475e-03 3.675654e-04 3.681127e-04 1.756676e-03
## 111 112 113 114 115
## 1.981103e-03 9.754931e-03 2.354276e-05 3.355610e-03 1.756504e-04
## 116 117 118 119 120
## 3.399336e-06 5.491710e-04 6.431870e-06 9.923681e-03 3.236055e-03
## 121 122 123 124 125
## 1.624381e-03 1.172468e-05 2.206231e-03 1.337213e-03 8.058774e-04
## 126 127 128 129 130
## 4.108480e-03 1.170423e-02 3.615455e-03 8.760133e-06 1.472871e-06
## 131 132 133 134 135
## 1.144466e-04 9.985317e-05 4.278511e-04 1.536422e-04 1.317295e-03
## 136 137 138 139 140
## 1.372503e-03 9.001797e-04 3.873307e-04 3.479622e-02 1.093127e-02
## 141 142 143 144 145
## 1.703842e-03 5.474786e-04 1.924143e-03 3.277167e-06 2.786034e-03
## 146 147 148 149 150
## 8.920424e-06 4.944636e-03 2.807581e-03 1.324993e-04 4.125021e-05
## 151 152 153 154 155
## 1.116912e-02 6.872314e-03 2.655669e-03 1.348741e-03 5.622060e-04
## 156 157 158 159 160
## 1.801882e-03 4.300273e-06 5.199456e-04 2.348412e-03 2.588558e-05
## 161 162 163 164 165
## 1.433510e-03 7.745445e-04 3.306319e-04 4.034340e-04 1.404673e-05
## 166 167 168 169 170
## 7.893235e-04 2.621461e-04 1.683682e-05 2.722357e-03 8.687618e-04
## 171 172 173 174 175
## 6.523981e-03 1.382915e-05 1.082414e-04 1.165182e-03 3.988461e-05
## 177 178 179 180 181
## 4.140182e-05 5.271212e-03 2.711268e-03 3.018363e-03 7.328011e-04
## 182 183 184 185 186
## 5.153066e-03 3.042363e-03 5.065314e-04 6.485450e-03 1.062737e-02
## 187 188 189 190 191
## 4.907789e-03 5.088367e-03 4.011871e-04 4.368638e-04 1.502905e-03
## 192 193 194 195 196
## 2.073765e-04 1.662333e-03 2.553593e-03 7.616832e-05 2.195589e-03
## 197 198 199 200 201
## 4.695773e-03 1.739894e-04 1.441452e-04 1.828951e-04 5.316878e-05
## 202 203 204 205 206
## 4.573369e-04 1.054271e-04 8.035693e-06 1.711428e-04 1.323312e-04
## 207 208 209 210 211
## 1.627571e-04 1.017564e-03 1.343025e-05 1.048791e-04 5.848871e-04
## 212 213 214 215 216
## 1.798831e-03 8.274625e-03 7.276398e-07 6.814074e-04 7.999788e-04
## 217 218 219 220 221
## 2.636695e-06 4.196595e-03 3.326340e-04 5.668468e-04 3.560563e-03
## 222 223 224 225 226
## 7.932861e-04 5.116409e-04 8.555473e-05 1.993805e-03 2.969881e-06
## 227 228 229 230 231
## 1.038617e-04 3.587097e-05 7.723367e-04 1.043787e-02 3.632631e-04
## 232 233 234 235 236
## 2.918906e-04 2.170598e-05 1.274902e-03 1.191147e-06 2.706881e-03
## 237 238 239 240 241
## 1.002980e-03 1.127884e-02 1.462014e-04 2.341247e-06 9.691864e-05
## 242 243 244 245 246
## 1.562080e-04 1.918112e-03 1.208516e-06 1.577807e-03 2.246451e-04
## 247 248 249 250 251
## 6.856845e-03 1.643265e-03 1.836275e-02 3.000762e-03 2.938401e-03
## 252 253 254 255 256
## 1.424394e-03 1.059559e-02 1.504406e-05 1.875266e-03 3.270413e-06
## 257 258 259 260 261
## 3.020612e-03 5.479769e-04 5.347724e-04 1.788675e-04 7.067421e-06
## 262 263 264 265 266
## 1.579329e-03 1.297818e-05 1.306728e-03 1.618743e-05 4.197649e-04
## 267 268 269 270 271
## 5.603899e-07 1.682458e-03 5.078914e-03 1.249098e-03 2.138688e-07
## 272 273 274 275 276
## 3.637804e-04 2.297152e-03 3.625006e-03 9.706161e-04 8.453090e-03
## 277 279 280 281 282
## 8.221500e-03 2.903182e-05 3.917443e-03 1.289357e-05 1.876943e-04
## 283 284 285 286 287
## 7.811538e-03 6.241586e-05 3.669516e-03 2.260326e-03 9.696378e-05
## 288 289 290 291 292
## 1.075501e-05 3.439622e-03 1.476867e-04 9.451931e-04 8.043664e-05
## 293 294 295 296 297
## 8.006605e-05 2.608237e-04 3.642120e-04 1.110590e-04 6.912347e-04
## 299 300 301 302 303
## 1.037926e-03 2.302189e-03 1.506446e-02 1.213464e-03 5.784579e-04
## 304 305 306 307 308
## 5.477090e-04 2.494791e-04 2.621553e-04 5.609695e-05 6.037795e-03
## 309 310 311 312 313
## 2.623062e-03 2.190796e-03 1.184799e-04 4.595411e-04 2.136557e-03
## 314 315 316 317 318
## 1.178762e-04 1.255140e-03 1.957706e-03 2.617487e-03 4.647854e-06
## 319 320 321 322 323
## 1.203079e-04 7.784063e-04 1.996550e-03 5.339854e-04 4.768896e-04
## 324 325 326 327 328
## 1.873916e-04 1.377090e-03 1.124370e-04 1.388773e-03 7.133237e-04
## 329 330 331 332 333
## 1.068561e-03 6.688153e-07 2.277190e-04 1.005425e-04 4.126710e-04
## 334 335 336 337 338
## 4.239403e-03 3.872964e-07 3.208166e-04 3.558723e-03 3.987121e-04
## 339 340 341 343 344
## 4.336547e-07 6.265775e-04 6.362877e-07 2.184722e-06 1.503205e-04
## 345 346 347 348 349
## 8.629488e-05 1.203576e-03 5.342945e-05 8.276439e-05 4.172393e-03
## 350 351 352 353 354
## 2.010043e-04 1.813412e-04 1.103757e-03 5.116216e-04 1.421534e-03
## 355 356 357 358 359
## 3.237523e-07 2.124335e-03 1.656522e-05 2.107369e-03 1.064613e-06
## 360 361 362 363 364
## 1.406517e-04 4.036877e-05 1.898873e-04 7.213794e-04 1.674341e-02
## 365 366 367 368 369
## 3.894949e-04 5.131893e-03 4.280909e-04 2.882945e-04 1.268574e-03
## 370 371 372 373 374
## 6.128398e-04 4.653312e-03 3.966617e-03 4.178548e-04 7.446793e-04
## 375 376 377 378 379
## 1.399947e-02 7.238569e-04 6.688734e-04 8.117083e-06 1.548044e-03
## 380 381 382 383 384
## 1.528814e-03 1.666879e-04 3.347214e-04 2.698099e-03 1.396226e-03
## 385 386 387 388 389
## 9.286380e-05 2.205523e-05 2.483743e-05 9.129923e-05 3.195493e-06
## 390 391 392 394 395
## 1.689474e-03 1.323054e-05 5.653313e-03 1.081766e-03 1.099372e-05
## 396 397 398 399 400
## 6.544350e-03 2.091592e-03 1.572124e-03 1.877792e-03 3.741160e-05
## 401 402 403 404 405
## 9.321803e-05 9.272344e-05 4.160715e-03 4.927077e-05 2.306507e-04
## 406 407 408 409 410
## 9.357719e-05 2.022122e-05 1.968139e-03 7.278751e-04 2.329951e-05
## 411 412 413 414 415
## 3.854759e-04 5.634831e-06 3.591673e-04 4.942919e-03 1.053912e-03
## 416 417 418 419 420
## 9.012352e-04 9.246236e-06 3.098641e-03 3.988597e-03 3.768479e-03
## 421 423 424 425 426
## 3.350123e-05 1.248138e-02 1.320237e-03 3.436121e-05 4.610486e-05
## 427 428 429 430 431
## 7.284765e-05 2.678897e-04 1.200142e-04 3.945567e-04 5.042197e-04
## 432 437
## 5.055682e-04 9.536790e-04
#Create histogram
#A density plot of the residuals
plot(density(resid(model4)))
#Create a QQ plot qqPlot(model, main="QQ Plot") #qq plot for studentized resid
leveragePlots(model4) # leverage plots
#Collinearity
vif(model4)
## sdata$toptim sdata$tmarlow sdata$tpstress
## 1.296847 1.087557 9.791870
## sdata$gender sdata$intgenstress
## 22.979404 27.390333
sqrt(vif(model4))
## sdata$toptim sdata$tmarlow sdata$tpstress
## 1.138792 1.042860 3.129196
## sdata$gender sdata$intgenstress
## 4.793684 5.233577